Well, they were an experienced, played-in unit from years of hard gigging (not least as Purple's often enough opening act on endless US tours, by the look of it, that vid is also from a Purple gig) and just replaced their guitarist (Steve Edwards was a nice guy, said Craig Gruber in an interview, but he never had any ideas unlike his Elf-predecessor Rod Feinstein and was generally a "less is more" Clapton-acolyte).
I always found that Rainbow's debut sounded more organic and grooving than the overrated, and even harshly-teutonic in its merciless beat, Rising 2nd album. The only thing better on the 2nd album was Carey's synth playing, mainly because his predecessor Mickey Lee Soule considered himself foremost a piano (and he was excellent in that) and not an organ, much less a synth player. However that is exactly what Blackmore wanted as that was what he had gotten from Jon Lord (who never played much piano within Purple) all these years and obviously wanted to retain. Blackmore doesn't mind a little piano, but let's not get carried away.
The Elf albums Carolina County Ball and Trying to Burn the Sun were excellent and are in dire need of a worthy remastered reissue (their debut wasn't bad, but still a little raw and formative). I loved the way Mickey Lee Soule's ivories and Gruber's bass playing embellished the songs and Trying to Burn the Sun did of course feature the great Mark Nauseef on added percussion. Hah, as I type this, my random CD function on the office hifi plays the IGB's Scarabus with Nauseef's formidable drumming!!!